I've tried to simplify it, simple enough to make my question clearer. The alert 'I am a boy' didn't popup with even after the addClass has been executed. Here is my code:
$(".first").click(function () {
var a = $(this).html();
if (a=='On') {
$(this).removeClass('first').unbind().addClass('second');
$(this).html('Off');
}
});
$(".second").click(function () {
alert('I am a boy');
});
<button class="first">On</button>